% Mizar problem: t17_msualg_6,msualg_6,751,52 fof(t17_msualg_6,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_msualg_6(A,C,D,B,E) => ( r1_rewrite1(k3_msualg_6(A),C,D) & m2_msualg_6(E,A,B,C,D) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_rewrite1,cc11_rewrite1,cc12_rewrite1,cc13_rewrite1,cc14_rewrite1,cc15_rewrite1,cc1_altcat_1,cc1_arytm_3,cc1_finseq_1,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_funct_7,cc1_msualg_1,cc1_msualg_6,cc1_pboole,cc1_relset_1,cc1_rewrite1,cc1_xreal_0,cc2_arytm_3,cc2_funct_1,cc2_funct_7,cc2_pboole,cc2_rewrite1,cc2_xreal_0,cc3_arytm_3,cc3_rewrite1,cc3_xreal_0,cc4_rewrite1,cc4_xreal_0,cc5_funct_2,cc5_rewrite1,cc5_xreal_0,cc6_funct_2,cc6_rewrite1,cc6_xreal_0,cc7_rewrite1,cc7_xreal_0,cc8_rewrite1,cc8_xreal_0,cc9_rewrite1,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,d1_funct_2,d1_tarski,d5_tarski,d6_msualg_6,dt_k10_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_finseq_4,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_msualg_6,dt_k4_finseq_1,dt_k4_funct_7,dt_k4_relset_1,dt_k4_tarski,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k9_finseq_1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_finseq_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_rewrite1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_msualg_6,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_finseq_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_rewrite1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_msualg_6,existence_m2_relset_1,existence_m2_subset_1,fc10_funct_7,fc10_xreal_0,fc11_finseq_1,fc11_xreal_0,fc12_finseq_1,fc12_xreal_0,fc17_finseq_1,fc1_finseq_1,fc1_msualg_1,fc1_struct_0,fc2_altcat_1,fc2_finseq_1,fc2_pboole,fc3_finseq_1,fc3_funct_7,fc3_xreal_0,fc4_finseq_1,fc4_funct_7,fc5_finseq_1,fc5_funct_7,fc6_funct_1,fc7_finseq_1,fc7_funcop_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_arytm_3,rc1_finseq_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_funct_7,rc1_msualg_6,rc1_partfun1,rc1_pboole,rc1_rewrite1,rc1_xreal_0,rc2_finseq_1,rc2_funct_1,rc2_funct_7,rc2_partfun1,rc2_pboole,rc2_rewrite1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_pboole,rc3_rewrite1,rc3_struct_0,rc3_xreal_0,rc4_finseq_1,rc4_funct_1,rc4_pboole,rc4_rewrite1,rc4_xreal_0,rc5_funct_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k2_finseq_4,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t11_msualg_6,t12_msualg_6,t16_rewrite1,t1_arithm,t1_numerals,t1_subset,t2_subset,t3_subset,t48_funct_7,t4_finseq_1,t4_subset,t55_finseq_1,t57_finseq_1,t5_subset,t61_finseq_1,t6_boole,t7_boole,t8_boole,t8_rewrite1]), [file(msualg_6,t17_msualg_6)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) ) ) ), file(rewrite1,cc10_rewrite1), []). fof(cc11_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) ) ) ), file(rewrite1,cc11_rewrite1), []). fof(cc12_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc12_rewrite1), []). fof(cc13_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v9_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc13_rewrite1), []). fof(cc14_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc14_rewrite1), []). fof(cc15_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v10_rewrite1(A) ) ) ), file(rewrite1,cc15_rewrite1), []). fof(cc1_altcat_1,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_fraenkel(B) ) ) ), file(altcat_1,cc1_altcat_1), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). fof(cc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v5_msualg_1(B,A) => v1_msualg_6(B,A) ) ) ) ), file(msualg_6,cc1_msualg_6), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ v1_xboole_0(B) ) ) ), file(rewrite1,cc1_rewrite1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). fof(cc2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) ) ), file(rewrite1,cc2_rewrite1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) => ( v1_relat_1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc3_rewrite1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc4_rewrite1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_rewrite1(A) ) ) ), file(rewrite1,cc5_rewrite1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc6_rewrite1), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc7_rewrite1), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v6_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc8_rewrite1), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v5_rewrite1(A) ) ) ), file(rewrite1,cc9_rewrite1), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) => ( m2_msualg_6(E,A,B,C,D) <=> ? [F] : ( m1_rewrite1(F,k3_msualg_6(A)) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) & v1_funcop_1(G) & E = k4_funct_7(k1_funct_1(u4_msualg_1(A,B),C),G) & k3_finseq_1(F) = k1_nat_1(k3_finseq_1(G),1) & C = k1_funct_1(F,1) & D = k1_funct_1(F,k3_finseq_1(F)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r2_hidden(H,k4_finseq_1(G)) & I = k1_funct_1(G,H) & J = k1_funct_1(F,H) & K = k1_funct_1(F,k1_nat_1(H,1)) ) => r1_msualg_6(A,J,K,B,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(msualg_6,d6_msualg_6), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_4(A,B,C),A) ) ), file(finseq_4,k2_finseq_4), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => m2_relset_1(k3_msualg_6(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(msualg_6,k3_msualg_6), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) ) => ( v1_relat_1(k4_funct_7(A,B)) & v1_funct_1(k4_funct_7(A,B)) ) ) ), file(funct_7,k4_funct_7), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(rewrite1,m1_rewrite1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_msualg_6,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m2_msualg_6(E,A,B,C,D) => ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) ), file(msualg_6,m2_msualg_6), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ? [B] : m1_rewrite1(B,A) ) ), file(rewrite1,m1_rewrite1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_msualg_6,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) ) => ? [E] : m2_msualg_6(E,A,B,C,D) ) ), file(msualg_6,m2_msualg_6), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_funct_7(k5_finseq_1(A)) ) ) ), file(funct_7,fc10_funct_7), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc2_altcat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_fraenkel(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ) ), file(altcat_1,fc2_altcat_1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_funct_7,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). fof(fc4_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) ) ) ), file(funct_7,fc4_funct_7), []). fof(fc5_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc5_finseq_1), []). fof(fc5_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) ) ) ), file(funct_7,fc5_funct_7), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc7_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc7_finseq_1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ), file(funct_7,rc1_funct_7), []). fof(rc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v5_msualg_1(B,A) & v1_msualg_6(B,A) ) ) ), file(msualg_6,rc1_msualg_6), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ), file(rewrite1,rc1_rewrite1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ), file(funct_7,rc2_funct_7), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). fof(rc2_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ), file(rewrite1,rc2_rewrite1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). fof(rc3_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc3_rewrite1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). fof(rc4_rewrite1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc4_rewrite1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_finseq_4(A,B,C) = k10_finseq_1(B,C) ) ), file(finseq_4,k2_finseq_4), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(t11_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_msualg_6(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_msualg_6(A,B,C,D,E) => ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C)) & m2_relset_1(E,k1_funct_1(u4_msualg_1(A,D),B),k1_funct_1(u4_msualg_1(A,D),C)) & k1_funct_1(u4_msualg_1(A,D),B) != k1_xboole_0 & k1_funct_1(u4_msualg_1(A,D),C) != k1_xboole_0 ) ) ) ) ) ) ) ), file(msualg_6,t11_msualg_6), []). fof(t12_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_msualg_6(A,B,C,D,E) => r2_hidden(k4_tarski(B,C),k3_msualg_6(A)) ) ) ) ) ) ) ), file(msualg_6,t12_msualg_6), []). fof(t16_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) => r1_rewrite1(A,B,C) ) ) ), file(rewrite1,t16_rewrite1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t48_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k1_relat_1(B),A) => k4_funct_7(A,k9_finseq_1(B)) = B ) ) ), file(funct_7,t48_funct_7), []). fof(t4_finseq_1,axiom, ( k2_finseq_1(0) = k1_xboole_0 & k2_finseq_1(1) = k1_tarski(1) & k2_finseq_1(2) = k2_tarski(1,2) ), file(finseq_1,t4_finseq_1), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t55_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k4_finseq_1(B) = k2_finseq_1(1) & k2_relat_1(B) = k1_tarski(A) ) ) ) ), file(finseq_1,t55_finseq_1), []). fof(t57_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k1_funct_1(B,1) = A ) ) ) ), file(finseq_1,t57_finseq_1), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t61_finseq_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k10_finseq_1(A,B) <=> ( k3_finseq_1(C) = 2 & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ), file(finseq_1,t61_finseq_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) => m1_rewrite1(k10_finseq_1(B,C),A) ) ) ), file(rewrite1,t8_rewrite1), []).